James Clerk Maxwell - poet, mathematician and the father of light

Albert Einstein said, ‘I stand not on the shoulders of Newton, but on the shoulders of James Clerk Maxwell’. A survey of top physicists ranked Maxwell as physicist number three of all time, after Einstein and Newton. His contributions range over electromagnetism, the kinetic theory of gases, thermodynamics, colour, and the strength of materials.

Up to the time of Maxwell, the world was understood in terms of physical forces. Maxwell provided the bridge between the old model and that of the twentieth century which is dominated by fields. And it was this model on which Einstein based much of his own revolutionary work.

Maxwell is said to have provided the foundations for our modern western society with this theory of electromagnetism. It has given us radio, television, mobile phones and more. As we celebrate 150 years since Maxwell published his theory, Sharon Carleton reflects on the life of Maxwell and asks why so few people are familiar with his achievements.

Duration: 28min 27sec

Broadcast:
Sat 28 Nov 2015, 12:30pm

Guests

Transcript

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Robyn Williams: As you heard, the natural link between poetry and maths was demonstrated just then. It's an algorithm, which brings us naturally to our final genius, James Clerk Maxwell. We're coming to the end of this International Year of Light, and one monumental anniversary for 2015 is this, the 150th anniversary of the electromagnetic equations that changed the world and set the stage for Einstein. Our resident Science Show genius Sharon Carleton tells the tale.

Sharon Carleton: Albert Einstein said, 'I stand not on the shoulders of Newton but on the shoulders of James Clerk Maxwell.'

Malcolm Longair: The thing about James Clerk Maxwell was he had this infinite curiosity for all things scientific, and his contributions range over electromagnetism, the kinetic theory of gases, thermodynamics, colour, mathematical formalisms, the figures, strength of materials, it's a fantastic contribution.

Sharon Carleton: A millennium poll of the world's top 100 physicists put Maxwell alongside Newton and Einstein as one of the top three scientists of all time.

Malcolm Longair: Up until the time of Maxwell, one was dealing with a mechanical world where everything was due to forces on what we call the classical large scale. What Maxwell did was to provide the essential bridge between that mechanistic model and the model that we use in the 20th century which is dominated by fields which are much more difficult things, they are much more intangible than the idea of particles. That's where the modern 20th century physics came from, that is why Einstein built on all aspects of Maxwell's work.

Sharon Carleton: Professor Malcolm Longair is an emeritus professor of natural philosophy at the Cavendish Laboratory in Cambridge. Maxwell is revered among physicists and mathematicians for basically laying the very foundations of our modern Western society. And yet he is almost unknown outside professional circles, even in his native Scotland. So why is Maxwell so little known in comparison with his achievements? Professor Longair:

Malcolm Longair: The real fundamental reason is that his contributions are not so easily understood to the layperson. Furthermore, Maxwell was very modest, he didn't publicise his discoveries the way that others did. For example, Einstein made hay from his great discoveries in relativity. And finally it took some time before Maxwell's theories were confirmed by experiment. Most of the experiments which confirmed his ideas took place after his death, which is a tragedy.

Sharon Carleton: James Clerk Maxwell was born in Edinburgh, Scotland, in 1831, to reasonably wealthy parents, John and Frances. His mother was nearly 40 when she had him, and supervised his early education. By all accounts, the young boy had a prodigious need to know about everything in the natural world and could also recite whole passages of Milton and the Bible before he was eight.

His mother died of stomach cancer at the age of 48. James would die of the same disease at the same age. First, his father hired a 16-year-old tutor who was a bully and a complete disaster. Eventually James was sent to the prestigious Edinburgh Academy. His lifelong friend, Peter Guthrie Tait said:

Reading: At school he was at first regarded as shy and rather dull. He made no friendships and spent his occasional holidays in reading old ballads, drawing curious diagrams and making rude mechanical models.

Sharon Carleton: But Dafty, as he was rather cruelly nicknamed, soon showed them his true colours, and by middle school he surprised everyone by winning the top prizes for both maths and English. He had his first scientific paper read to the Royal Society of Edinburgh when he was still a schoolboy.

Malcolm Longair: He was brought up in a family which was very interested in science. They had a huge range of scientific toys in the house. So he produced his first paper at the age of 14 or 15, and it was published by the Royal Society of Edinburgh, but he was far too young to actually present it, it was presented by Professor Forbes on his behalf. And again, these papers are geometrical, showing how you can produce ovals, ellipses, all sorts of figures by simple geometric constructions.

Sharon Carleton: The cygnet went first to Edinburgh University so that he could stay close to his widowed father. But soon it became clear that with his mathematical abilities, his true academic home was Cambridge. His undergraduate friends there acknowledged him as the only man of genius amongst them. He shared the Smith Prize, the highest maths honour that Cambridge University could bestow. He became a fellow of Trinity College when only 23, and his father, with whom he was very close, died the following year.

Maxwell had been interested in the science of colour and light since he was a child, and now at Trinity he set about studying it seriously. He wanted to know why mixing different colours of light produced a different result to mixing the same colours of paint.

Malcolm Longair: What he did was to take the three-colour theory of Young and Helmholtz, which said that you only need three colour receptors to create all the colours, but they didn't know how to mix them and they didn't know what the primary lights were that you had to mix. So the early experiments were designed to show how much of, say, red, blue and green you have to mix to produce any colour in the spectrum.

Sharon Carleton: Biographer Lewis Campbell:

Reading: When experimenting at the window with his colour box, he excited the wonder of his neighbours who thought him mad to spend so many hours in staring into a coffin.

Malcolm Longair: Once he had got his three-colour system worked out, then he realised that if you took images through the three colours, through filters, then if you then projected back the light through the same filters onto a screen, if you aligned then the three projectors, then you would get a colour image, and that was the first time that was done. This is the origin of what you could call now the three-colour standard system that we use, every mobile phone, every television screen uses the same principles that Maxwell enunciated in his great papers of the 1860s.

Sharon Carleton: James Clerk Maxwell's science was well ahead of his contemporaries. On the other hand, he was also very much a man of his time. He was both extremely religious and an inveterate poet.

Daniel Brown: Maxwell is an astonishingly brilliant man and he is not to be underestimated as a poet.

Sharon Carleton: Daniel Brown is an English professor at Southampton University in England, but he is originally from Perth.

Daniel Brown: He is very witty, he has huge imagination and huge creativity which we know best through his science. But it is equally evident in his poetry, integral to the politics and the cultures of science that he participated in so vigorously, and really foundational to his science through the sense of play.

Sharon Carleton: With the formation of the British Association for the Advancement of Science in 1831, we see the beginnings of science as a profession, and the lobbying for specific science education.

Daniel Brown: Professional science becomes masculine because the British Association makes a controversial decision not to allow women as full members, and poetry was very much used to bond groups of men against other factions of scientists. So Maxwell belongs to a Scots Presbyterians group. They were opposed to another group of what they saw as upstarts, which are the metropolitans from London, which included TH Huxley, who is known as 'Darwin's bulldog', and its principal character John Tyndall who was professor of natural philosophy or physics at the Royal Institution. And he gave public lectures, very, very fashionable public lectures that Queen Victoria went to, George Eliot the novelist went to.

Tyndall was particularly notorious for his theory that everything was matter. It all comes down to little atoms which formed themselves. There's no need for God or anything else, the atoms were on automatic pilot and they attract each other and come together and form the whole world. So because this is the hypothesis that Maxwell and his Scots Presbyterian friends didn't like at all. It's against their Christian faith. One of them from 1871 called 'A Tyndallic Ode', it's written to be delivered at the 1871 annual meeting of the British Association for the Advancement of Science at Edinburgh, and they are attacking Tyndall with a sort of mock lecture in verse. In the second stanza it begins:

So this characterises Tyndall's atoms and identifies him with his atoms the way they come together to form everything, but it's characterised sexually. So the atoms come together as if they are lascivious, they are full of lust. They are sinners basically, burning in hell. And this also is a reference to Tyndall's rather scandalous reputation, very much the ladies' man and undermining him as a sort of sexually louche character.

Sharon Carleton: And what does this really say about Maxwell's character, that he is doing this publicly?

Daniel Brown: It was a tradition amongst this very masculine culture where you sort of bond around your enemies, poke gentle fun at one another. So it's not actually vicious and wasn't perceived as too vicious. The difficulty is that Maxwell is very, very witty and he is actually a good poet, so he can be very savage.

Sharon Carleton: In 1856 Maxwell took up a post as professor of natural philosophy at Marischal College in Aberdeen. He lived there for the six months of the academic year and spent the holidays at his family estate, Glenlair, 420 kilometres north, which he had inherited from his father. James was 25, and the next youngest professor was 40. And despite being welcomed, he felt his quirky humour would not be appreciated.

Reading: No jokes of any kind are understood here. I've not made one for two months, and if I feel one coming on I shall bite my tongue.

Sharon Carleton: Maxwell gave lectures and had plenty of time for his own research. He had become fascinated by a problem that had vexed researchers for 200 years. What exactly made up the rings of Saturn? Were they solid, were they liquid? A year before, Cambridge had announced that this was the research topic for its impressive £130 Adams Prize. It was Maxwell's work on the dynamics of Saturn's rings of that first brought him to national and international attention.

Reading: I am still at Saturn's rings. At present two rings of satellites are disturbing one another. I have devised a machine to exhibit the motions of the satellites in a disturbed ring for the edification of sensible image worshippers.

Sharon Carleton: Andrew Jacob, Sydney Observatory:

Andrew Jacob: He simply sat down, and as a good mathematician and a good researcher worked through it step by step. He took the suggestions that it could be a solid ring and analysed it with the mathematics of the times, some important differential equations and some reasonably complex mathematics, to step by step take apart each of the suggestions. And one by one he eliminated the solid ring and the liquid ring and ended up with the conclusion that it had to be a series of separate particles surrounding Saturn, each in their own orbit.

Sharon Carleton: And was that original, totally original?

Andrew Jacob: Not completely original. It had been suggested earlier on by Cassini that it might be a swarm of particles, a swarm of small moons around Saturn, but there was no real rigorous backup to that in terms of the science or the mathematics or the analysis. What Maxwell did was really put it all together in a really carefully, rationally argued, beautifully clear essay of around about 70 pages. And it was very, very convincing for everybody at the time.

Sharon Carleton: The Astronomer Royal, Sir George Biddell Airy, said it was one of the most remarkable applications of mathematics to physics that he'd ever seen. Maxwell won the Adams Prize. His was the only entrant, as no one else had made enough headway to even enter the competition. His final article on the stability of the motion of Saturn's rings was published by the Scottish Royal Society in 1859. Maxwell's model of Saturn and her rings still resides at the Cavendish Laboratory in Cambridge. Professor Malcolm Longair is a former Astronomer Royal of Scotland and former head of the Cavendish.

Malcolm Longair: Astronomers basically accepted what he had said. He demonstrated it couldn't be a solid disc, it couldn't be a gaseous disc, it had to be a disc of discrete particles interacting gravitationally in a disc.

Sharon Carleton: Now, how did that lead on to his kinetic theory of gases?

Malcolm Longair: Once you have the idea of being able to treat the mechanics of the particles, then he went back to his other interests, which had come from the earliest times, of trying to understand the details of the kinetic theories of gases. That's where the particles bang into each other and create the properties of gases as we know it. Already there were very important work done by Clausius earlier in the century who had worked on a good version of the theory of gases, but he couldn't work out exactly what the distribution of speeds in the gas molecules were. And so that's where Maxwell started making his great contributions. He was interested in prolating the kinetics of particles to the big properties of what we call the macroscopic properties of gases that we would measure with our instruments.

Sharon Carleton: And how did the scientists take that?

Malcolm Longair: Well, in fact during his lifetime and immediately after, this was the work for which Maxwell was most famous. He was regarded as being one of the great pioneers of the kinetic theory to understand the properties of gases and its relationship to basic thermodynamics.

Sharon Carleton: Well, that was his other big interest, wasn't it, thermodynamics.

Malcolm Longair: Absolutely, yes. Once he had got the idea that there has to be a statistical distribution of speeds in a gas, what is known as the Maxwell distribution, he realised immediately that this was the same as the distribution of errors that you will get in random processes. And so what it meant was that you no longer had a completely determinate theory of what the outcome of the pressure of a gas would be that you could predict entirely according to classical theory. And Maxwell is absolutely clear about this from the very beginning, that you cannot derive by a mechanical model what we call the second law of thermodynamics, namely that the randomness will continue. They couldn't get that right, you had to introduce the statistical concepts, and that's absolutely fundamental.

Sharon Carleton: And all this work basically led to a whole new branch of physics, didn't it, and understanding upper atmospheres and space.

Malcolm Longair: Yes. This was the beginning of the great revolution which led to the disciplines of statistical mechanics. That is to say, how can you handle mathematically the properties of huge, huge numbers of particles, 1023 particles, how do they behave? It's very different from individual single particles banging into each other. But that of course is the basis of all the phenomena of modern physics where we are just taught from the very beginning you must understand the various sorts of statistical distributions which lead to the properties of gases, liquids, solids and everything else.

Sharon Carleton: There's a lot of conjecture about Maxwell's personal life. He was a very private man. One biographer notes that he had always been particularly fond of his cousin Lizzie. On a family holiday when she was 14 and he was 23, they declared their love and determined to be married when she turned 16 - not uncommon in those days. But it was not to be. Both families thought it was a little too close for comfort, and they agreed to part.

A couple of years later at Marischal College, Maxwell met and later married the principal's daughter, Katherine Dewar. They never had children, shared a deep religious faith and worked together on his experiments in Aberdeen and later in London. Daniel Brown:

Daniel Brown: Later on he writes poems that refer to her. His science poems, he has one on using a galvanometer which measures electric current. It is at once scientific, and of course he loves the romance of science, and he liked to share it with his wife. They could enjoy the more basic experience and wonder of science and scientific and physical phenomena. So here's an extract from Maxwell's poem, 'A Lecture on Thomson's galvanometer: delivered to a single pupil in an Alcove' which was published in Nature magazine in 1872:

So it looks a bit dodgy on the face of it, a lecture in an alcove delivered to a single pupil, and 'single' seems very charged here, like a single woman, it does look a bit sleazy, and it's set up to provoke contemporary anxieties about women studying science. It was included in Nature as part of this editorial debate at the time about whether women should be allowed to go to university lectures on science and study science. But it is actually based on his experience with his wife in their laboratory, so it's all above board.

Reading: Science is incompetent to reason upon the creation of matter itself out of nothing. We have reached the uppermost limits of our thinking faculties. When we have admitted that because matter cannot be eternal and self-existent, it must have been created.

Sharon Carleton: James and Katherine moved back to London where he took up the post of Professor of Natural philosophy at Kings College. He was awarded the Royal Society's Rumford Medal for his work on colour, and was elected to the Society the following year.

His theory of electromagnetic radiation, whose 150th anniversary we are commemorating, was one of the greatest intellectual achievements of the 19th century. According to Professor Malcolm Longair, Maxwell's theory was the essential link between Newton and Einstein. Einstein, who was born in the same year as Maxwell died, said of this theory, 'This change in the conception of reality is the most profound and the most fruitful that physics has experienced since the time of Newton.'

Reading: On 16 June, 1865, James Clerk Maxwell's paper 'A Dynamical Theory of the Electromagnetic Field' was sent to the printers. Six days earlier, Richard Wagner's Tristan und Isolde had its world premiere in Munich. The word 'revolutionary' is the only adjective which begins to do justice to the extraordinary impact of these two events, one the physical sciences, the other in music, opera and drama.

Wagner's staggering innovations revolutionised the approaches of composers. Music would never be the same again. In exactly the same way, Maxwell's monumental paper laid the foundations for the innovations of 20th century physics by placing fields at the heart of the theory of electromagnetism and of all subsequent fields which describe how matter and radiation behave at a fundamental level.

Malcolm Longair: It is an absolutely tremendous piece of work, and what it did was to produce the set of mathematical equations which describe how classical electric and magnetic fields and currents and voltages and everything are all tied together in one beautiful symmetric framework. The big leap which he made was to realise that you had to abandon this particle picture and take very seriously the idea that there are fields in the vacuum, and that's where things become difficult to explain. What do we mean by fields in a vacuum? But what he was absolutely clear about is that he really meant that there was something in the vacuum caused by electromagnetic phenomena. Once the next generation got hold of the idea of fields, that became the normal language of physics, and that led to Einstein's great discoveries of general relativity and so on.

Reading: The theory I propose may be called a theory of the electromagnetic field because it has to do with the space in the neighbourhood of the electric and magnetic bodies. And it may be called a dynamical theory because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced. Until I am convinced to the contrary, I hold it to be great guns.

Malcolm Longair: It was not immediately obvious to people, the significance of this theory. There were many other theories afloat at the time by very distinguished physicists, and it was only almost 10 years after Maxwell's death that the key experiments were carried out by Hertz which demonstrated that electromagnetic disturbances have all the properties of light. But once that had happened, everyone very quickly adopted Maxwell's theory and it became the standard theory of electromagnetism.

Sharon Carleton: In 1865, James resigned from Kings College and returned with Katherine to the peace and green beauty of Glenlair. He wrote more than 100 scientific papers during his relatively short life, including 'On the Rigidity of Lattice', 'On the Theory of Heat', and 'On Matter and Motion', which was lauded at the time as:

Reading: The ablest introduction to mechanics ever published.

Sharon Carleton: In 1871, Maxwell received an offer he couldn't refuse, and with Katherine, headed back to London. Maxwell became the first Cavendish professor at Cambridge, with responsibility for setting up the now world-famous Cavendish Laboratory. Just think, the discoveries of electrons, neutrons, pulsars and the structure of DNA. Maxwell designed specific apparatus to test his theory of electromagnetism, but died before it could be confirmed.

So what was Maxwell's Cavendish legacy? Malcolm Longair, also a former head of the Cavendish Laboratory:

Malcolm Longair: He bought all the apparatus, he started off the research program from absolutely zero. And he never lived to see the full consummation of his ideas, but his subsequent Cavendish professors—and that's the names of Rayleigh, JJ Thomson, Rutherford and Bragg—they followed in Maxwell's tradition of combining experiment and theory to understand the nature of matter.

Sharon Carleton: James Clerk Maxwell died on 5 November, 1879, from the same abdominal cancer that had killed his mother. He was 48 years old.

Malcolm Longair: Maxwell for me (and it's not just because I'm 100% Scottish), he really is up there with the greatest minds in the physical sciences that there have ever been. There is no question in my mind that he is on a par with Newton and Einstein in the significance of their contributions to understanding the way that the world works. And without their works we wouldn't have the civilisation that we have, we wouldn't have all the electronic industries, we wouldn't have our ability to understand the way the world works and what we should do to make it better and preserve it for future generations.

Robyn Williams: That portrait of James Clerk Maxwell was written and presented by Sharon Carleton, production by David Fisher, with Joe Wallace. Readings by Angus McDonald and David Thomson.

And there's a marvellous piece on Maxwell in Cosmos magazine just out this week, written by Robyn Arianrhod of Monash University in Melbourne. Cosmos, with a dog smiling on the cover.